To find the coordinates of the other endpoint, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) is given by the average of the x-coordinates and the average of the y-coordinates.
Given that the midpoint E is (-1, 0) and one endpoint C is (5, 2), we can let the coordinates of the other endpoint be (x, y).
The x-coordinate of the midpoint is the average of the x-coordinates of C and (x, y):
(-1) = (5 + x)/2
Multiplying both sides by 2, we have:
-2 = 5 + x
Subtracting 5 from both sides, we get:
x = -7
The y-coordinate of the midpoint is the average of the y-coordinates of C and (x, y):
0 = (2 + y)/2
Multiplying both sides by 2, we have:
0 = 2 + y
Subtracting 2 from both sides, we get:
y = -2
Therefore, the coordinates of the other endpoint are (-7, -2).
For the second problem, the coordinate of the midpoint of PB¯¯¯¯¯ can be found by taking the average of the coordinates of the endpoints -2 and 12.
The midpoint is given by:
Midpoint = (Endpoint₁ + Endpoint₂)/2
Midpoint = (-2 + 12)/2
Midpoint = 10/2
Midpoint = 5
Therefore, the coordinate of the midpoint of PB¯¯¯¯¯ is 5.
The distance formula is a formula used to find the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem. The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Using the distance formula, we can calculate the distance between point A(1, 1) and point B(7, -7):
Distance = √((7 - 1)² + (-7 - 1)²)
Distance = √(6² + (-8)²)
Distance = √(36 + 64)
Distance = √100
Distance = 10
Therefore, the distance between point A(1, 1) and point B(7, -7) is 10.
Enter your answer and show all the steps that you use to solve this problem in the space provided. The midpoint of CD¯¯¯¯¯ is E(−1,0) . One endpoint is C(5,2) . What are the coordinates of the other endpoint?
Enter your answer and show all the steps that you use to solve this problem in the space provided. PB¯¯¯¯¯ is a line segment on a number line. It has endpoints at −2 and 12. What is the coordinate of its midpoint? (2 points)
Enter your answer and show all the steps that you use to solve this problem in the space provided. Explain the distance formula. Then use it to calculate the distance between A(1, 1) and B(7,−7)
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